# American Institute of Mathematical Sciences

• Previous Article
Local solutions in Sobolev spaces and unconditional well-posedness for the generalized Boussinesq equation
• CPAA Home
• This Issue
• Next Article
The number of limit cycles for generalized Abel equations with periodic coefficients of definite sign
September  2009, 8(5): 1503-1520. doi: 10.3934/cpaa.2009.8.1503

## The dimension of the attractor for the 3D flow of a non-Newtonian fluid

 1 Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, 186 75 Prague 8 2 Mathematical Institute, Charles University, Sokolovská, 83, CZ-18675 Prague 8, Czech Republic 3 Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Prague 8 4 Department of Mathematical Analysis, Charles University, Prague, Sokolovská 83, 186 75 Prague 8

Received  August 2008 Revised  January 2009 Published  April 2009

The equations of an incompressible, homogeneous fluid occupying a bounded domain in $\mathbb R^3$ are considered.
The stress tensor has a general polynomial dependence on the symmetric velocity gradient. The goal is to estimate the dimension of the global attractor in terms of relevant physical constants.
Citation: M. Bulíček, F. Ettwein, P. Kaplický, Dalibor Pražák. The dimension of the attractor for the 3D flow of a non-Newtonian fluid. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1503-1520. doi: 10.3934/cpaa.2009.8.1503
 [1] Hafedh Bousbih. Global weak solutions for a coupled chemotaxis non-Newtonian fluid. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 907-929. doi: 10.3934/dcdsb.2018212 [2] Linfang Liu, Tomás Caraballo, Xianlong Fu. Exponential stability of an incompressible non-Newtonian fluid with delay. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4285-4303. doi: 10.3934/dcdsb.2018138 [3] Jong Yeoul Park, Jae Ug Jeong. Pullback attractors for a $2D$-non-autonomous incompressible non-Newtonian fluid with variable delays. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2687-2702. doi: 10.3934/dcdsb.2016068 [4] Guowei Liu, Rui Xue. Pullback dynamic behavior for a non-autonomous incompressible non-Newtonian fluid. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2193-2216. doi: 10.3934/dcdsb.2018231 [5] Jin Li, Jianhua Huang. Dynamics of a 2D Stochastic non-Newtonian fluid driven by fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2483-2508. doi: 10.3934/dcdsb.2012.17.2483 [6] Aneta Wróblewska-Kamińska. Local pressure methods in Orlicz spaces for the motion of rigid bodies in a non-Newtonian fluid with general growth conditions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1417-1425. doi: 10.3934/dcdss.2013.6.1417 [7] Li Fang, Zhenhua Guo. Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid. Communications on Pure and Applied Analysis, 2017, 16 (1) : 209-242. doi: 10.3934/cpaa.2017010 [8] Shengfan Zhou, Min Zhao. Fractal dimension of random attractor for stochastic non-autonomous damped wave equation with linear multiplicative white noise. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2887-2914. doi: 10.3934/dcds.2016.36.2887 [9] Lars Diening, Michael Růžička. An existence result for non-Newtonian fluids in non-regular domains. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 255-268. doi: 10.3934/dcdss.2010.3.255 [10] Yukun Song, Yang Chen, Jun Yan, Shuai Chen. The existence of solutions for a shear thinning compressible non-Newtonian models. Electronic Research Archive, 2020, 28 (1) : 47-66. doi: 10.3934/era.2020004 [11] Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Michael Z. Zgurovsky. Strong attractors for vanishing viscosity approximations of non-Newtonian suspension flows. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1155-1176. doi: 10.3934/dcdsb.2018146 [12] Mohamed Tij, Andrés Santos. Non-Newtonian Couette-Poiseuille flow of a dilute gas. Kinetic and Related Models, 2011, 4 (1) : 361-384. doi: 10.3934/krm.2011.4.361 [13] Jan Sokołowski, Jan Stebel. Shape optimization for non-Newtonian fluids in time-dependent domains. Evolution Equations and Control Theory, 2014, 3 (2) : 331-348. doi: 10.3934/eect.2014.3.331 [14] Changli Yuan, Mojdeh Delshad, Mary F. Wheeler. Modeling multiphase non-Newtonian polymer flow in IPARS parallel framework. Networks and Heterogeneous Media, 2010, 5 (3) : 583-602. doi: 10.3934/nhm.2010.5.583 [15] Aneta Wróblewska-Kamińska. Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2565-2592. doi: 10.3934/dcds.2013.33.2565 [16] Emil Novruzov. On existence and nonexistence of the positive solutions of non-newtonian filtration equation. Communications on Pure and Applied Analysis, 2011, 10 (2) : 719-730. doi: 10.3934/cpaa.2011.10.719 [17] Pitágoras Pinheiro de Carvalho, Juan Límaco, Denilson Menezes, Yuri Thamsten. Local null controllability of a class of non-Newtonian incompressible viscous fluids. Evolution Equations and Control Theory, 2021  doi: 10.3934/eect.2021043 [18] Bum Ja Jin, Kyungkeun Kang. Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4815-4834. doi: 10.3934/dcds.2017207 [19] Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037 [20] Xin Liu, Yongjin Lu, Xin-Guang Yang. Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids. Evolution Equations and Control Theory, 2021, 10 (2) : 365-384. doi: 10.3934/eect.2020071

2020 Impact Factor: 1.916

## Metrics

• PDF downloads (79)
• HTML views (0)
• Cited by (3)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]